Volume of Prisms — pack the box, find the space inside!
This WebQuest is designed for one 45–60 minute period. Suggested breakdown: Learning Target + Introduction (5 min) → Process Steps 1–3, integer prisms (15 min) → 3D game (10 min) → Fraction edges + Step 4 (10 min) → Self-Check + NTKit quiz (10 min) → Reflection (5 min).
Think-Pair-Share works well for Steps 1–3. Pairs can build prisms with physical unit cubes or use the 3D game cooperatively. The Self-Check and NTKit quiz must be completed individually for grading.
Welcome to the Volume Vault! 📦 Your job is to fill boxes (called rectangular prisms) with little unit cubes.
Volume tells you how much space is inside a box. We measure it in cubic units (like cm³ or in³). The more cubes that fit inside, the bigger the volume.
In this WebQuest, you will find the volume of prisms with whole-number and fractional edge lengths.
By the end, you will be able to:
Do the steps in order. Read each one carefully.
Volume = the space inside a box. Unit cube = one small cube that is 1 unit on each side. Cubic units = how we count volume. A rectangular prism has three measurements: length (l), width (w), and height (h).
First multiply length × width to count the cubes in the bottom layer. Then multiply by height to stack the layers on top of each other.
Example: A box that is 3 × 2 × 4 → bottom layer = 6 cubes → × 4 layers = 24 cubic units.
Open the Volume Vault 3D game (link in Resources). Pack each prism with unit cubes and watch the volume add up. Notice how each new layer adds the same number of cubes.
A box can have a side like ½ unit. The same formula still works.
Example: 4 × 3 × ½ = 12 × ½ = 6 cubic units.
Think of it this way: you are stacking half-cubes, so the total is half of what a full layer would be.
Complete the Self-Check below (instant feedback), then fill in the NTKit grading quiz and save as PDF or DOC to turn in.
Use these to help you:
| Skill | 4 — Expert | 3 — Proficient | 2 — Developing | 1 — Beginning |
|---|---|---|---|---|
| Identify l, w, h of a prism | Names all three dimensions correctly every time; can label a diagram. | Names the dimensions correctly most of the time. | Identifies some dimensions; confuses width and height occasionally. | Needs step-by-step help to identify dimensions. |
| Apply V = l × w × h (whole numbers) | Calculates volume quickly and correctly; explains the formula. | Calculates volume correctly with minor arithmetic slips. | Sets up the formula correctly but makes multiplication errors. | Cannot yet apply the formula without teacher guidance. |
| Apply V = l × w × h (fractions) | Finds volume with fractional edges accurately; explains the reasoning. | Finds volume with fractions; few errors. | Some fraction volume answers correct; struggles with the fraction step. | Fraction volume not yet attempted correctly. |
| Explain unit cubes and packing | Explains clearly why volume = layers × cubes per layer. | Can explain the packing idea with minor gaps. | Understands that cubes fill the box; cannot explain why V = l × w × h. | Does not yet connect cubes to the formula. |
| Quiz score | 5/5 — 100% | 4/5 — 80% | 2–3/5 — 40–60% | 0–1/5 — below 20% |
Great work, vault keeper! You can now find the volume of a rectangular prism with V = l × w × h — even when the sides are fractions. These skills help you pack boxes, fill fish tanks, and measure real space.
Answer each question, then press Check This Answer for instant feedback.
Answer all 5. Then press Check My Answers. Type numbers only when asked.
Your score and a ✓/✗ for each question will appear in the panel above. Then use Save as PDF or Save as DOC to turn it in.
Answer both questions in your own words. Write in complete sentences.
1. Explain in your own words why the formula V = l × w × h works. Use the idea of layers and unit cubes.
2. Describe one real-world situation where you would need to find the volume of a rectangular prism. Why would volume matter in that situation?